# Quantum Access Structure and Secret Sharing

## TL;DR

This paper introduces a new decomposition method for quantum access structures, enabling more efficient quantum secret sharing schemes with reduced quantum shares and costs.

## Contribution

It defines minimal maximal quantum access structures and provides a construction method for general quantum access structures, improving efficiency over existing schemes.

## Key findings

- Reduced quantum shares in secret schemes
- New decomposition technique for quantum access structures
- Established necessary and sufficient conditions for minimal maximal structures

## Abstract

In this paper we define a kind of decomposition for a quantum access structure. We propose a conception of minimal maximal quantum access structure and obtain a sufficient and necessary condition for minimal maximal quantum access structure, which shows the relationship between the number of minimal authorized sets and that of the players. Moreover, we investigate the construction of efficient quantum secret schemes by using these techniques, a decomposition and minimal maximal quantum access structure. A major advantage of these techniques is that it allows us to construct a method to realize a general quantum access structure. For these quantum access structures, we present two quantum secret schemes via the idea of concatenation or a decomposition of a quantum access structure. As a consequence, the application of these techniques allow us to save more quantum shares and reduce more cost than the existing scheme.